The leading term of the Plancherel-Rotach asymptotic formula for solutions of recurrence relations
- M.V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow (Russian Federation)
Recurrence relations generating Padé and Hermite-Padé polynomials are considered. Their coefficients increase with the index of the relation, but after dividing by an appropriate power of the scaling function they tend to a finite limit. As a result, after scaling the polynomials 'stabilize' for large indices; this type of asymptotic behaviour is called Plancherel-Rotach asymptotics. An explicit expression for the leading term of the asymptotic formula, which is valid outside sets containing the zeros of the polynomials, is obtained for wide classes of three- and four-term relations. For three-term recurrence relations this result generalizes a theorem Van Assche obtained for recurrence relations with 'regularly' growing coefficients. Bibliography: 19 titles.
- OSTI ID:
- 22364154
- Journal Information:
- Sbornik. Mathematics, Vol. 205, Issue 12; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
Similar Records
A family of Nikishin systems with periodic recurrence coefficients
An asymptotic formula for polynomials orthonormal with respect to a varying weight. II